BUITEMS

BUITEMS
Quality & Excellence in Education
Rational Design of Retaining Walls
P
opt
=
1
2aN
i=
1
3
bN
[ i ] [ 5 - ( i -1) 4 ( 1) ]
5 + i -
4 3
N
2
4
3L
i -
2
i=
1 ( EI )
i
5L
2L
N
4
2N
1
( EI
[ i
3 - ( i -1) ]
3
)
In the particular case q 1 =q 2 =q, а N=1. P
i
opt
(3.6)
= 0,375 qL , (3.7)
which coincides with the result, obtained in [5]. Since the system is statically indeterminate to the first degree
P = + , (3.8)
P P
opt f ps
Where P f – selftensile force,
P ps – pre-tensioning force.
P = P - P , (3.9)
Hence, the required value of pre-tensioning force of anchor is equal to
ps opt f
selftensile force defined by force method
D 1p
P
f
= - , (3.10)
d
d
L
11
3 N
= 11 3
3N
i= 1
1
( EI )
i
2
(3i - 3 i + 1)
5
5 Nb 4
4
[ i - ( i -1)
] + [ i - ( i -1)
]
5
L
N 1 a
D
1p
= -
.
5
N i=
1 (EI ) i 5
4L
The primary structure of force method and moment diagrams are shown in Figure 3.1. Finally
N
1 a
[ bN
i
5 - ( i -1) ] [ 5 + i
4 - ( i -1) ]
4
3L
2 i=
1 ( EI )
i
5 4 L
Pf =
2
N
1
( ( ) 3 2
i - 3 i + 1)
(3.11)
N
i=
1 EI
i
Comparing the expressions (3.6) and (3.11) can be noted that P
opt
= Pf
, (3.12)
and as result P = 0 ps ;
This result is very interesting and shows that in the case of condition (3.1) pre-tension of anchor is not required.
The general solution is an iterative procedure consisting of two cycles. The external cycle implements a consistent
change in the force of pre-tensioning of anchor until performance of condition:
P m m-1
- P £ e , (3.13)
ps
ps
where m - number of external iteration, ε - given accuracy.
As initial approximation, is taken distribution of heights of wall sections, which found for cantilever system by
(1.19) (1.20). Further, the internal iteration cycle is executed, generated by (1.10) (1.19) (1.20). The analysis of
system was done by using PC "LIRA". The results of formation of geometry of wall by (1.10) are shown in Fig. 3.2
3.2. Dependence "height wall of section - height of
wall," as defined by (3.10) in the wall with anchor: eu -
ultimate SED, e - actual SED.
3.3. Dependence "SED per unit length - height of wall,"
as defined by (3.10) in the wall with anchor: e u -
ultimate SED, e - actual SED.
As seen from the graphs, the anchor reduces the height of section of equally strength wall by 41.5%, and changes,
the qualitative nature of its height.
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